Heretofore, a flow rate control apparatus has been known, which is connected by piping to a fluid pressure device such as a cylinder or the like, and which is capable of controlling operation of the fluid pressure device by adjusting the flow rate of a fluid, which is supplied to and discharged from the fluid pressure device. Such a flow rate control apparatus, for example, as disclosed in Japanese Patent No. 4292233, is equipped with a body having ports therein, and a needle valve that is screw-engaged with respect to the body. By rotation of the needle valve and displacement thereof in the axial direction, the flow rate of a fluid that flows between the body and a tapered needle provided on an end of the needle valve is controlled, whereby the fluid is made to flow from one of the ports to the other port.